III.4.2. Introduction :
III.4.2.1. Law of Snyell-Descartes:
The principle of the wave guide is included into the laws of Snyell-Descartes (Rene Descartes,
1596-1650) in geometrical optics. It is inspired by the third law on the principle of the refraction and the
critical angle of incidence according to the formulaviii :
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Figure 9: interface of two fields with different
A wave guide concentrates the rays of light in an environment of index n1, in an other
environment of index n2 < n1.
The rays of light, which come to the environment of index n1, penetrate into this environment. In
contact with the index n2, a part of the rays is reflected by this environment, and the other part is
However, when the incidence angle is higher than the critical incidence angle, the rays are totally
reflected. We can calculate this critical incidence angle according to the values of the indexes of the
different environments. By definition, the critical incidence angle an angle qi such as qr = Pi/2 radians,
then sin (qr) = 1. We deduct the critical angle of incidence from it:
q(i) = arcsin n(2)
Each time that a ray from the environment of index n1 comes to the border made with the other
environment of index n2, with an incidence angle higher than the critical incidence angle, this ray will be
concentrated in the environment of index n1 (figure 11). We can obtain a waves guide (figure 12).
Finally, the bigger the index difference between two environments, the weaker the critical
III.4.2.2. Our waves guides:
The waves guides we wanted to obtain will have two different index values. We wish to make
some parallelepipedal shape with a cylinder inside, playing the role of the second environment. The index
of the internal environment (cylinders) must be higher than the one of the parallelpipedal shape.
We wish to realize these two environment in gels. To obtain an index difference, we just have to
change the gel concentration: the more concentrated the gel, the higher the index.